# A Class-Kriging Predictor for Functional Compositions with Application to Particle-Size Curves in Heterogeneous Aquifers

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## Abstract

This work addresses the problem of characterizing the spatial field of soil particle-size distributions within a heterogeneous aquifer system. The medium is conceptualized as a composite system, characterized by spatially varying soil textural properties associated with diverse geomaterials. The heterogeneity of the system is modeled through an original hierarchical model for particle-size distributions that are here interpreted as points in the Bayes space of functional compositions. This theoretical framework allows performing spatial prediction of functional compositions through a functional compositional Class-Kriging predictor. To tackle the problem of lack of information arising when the spatial arrangement of soil types is unobserved, a novel clustering method is proposed, allowing to infer a grouping structure from sampled particle-size distributions. The proposed methodology enables one to project the complete information content embedded in the set of heterogeneous particle-size distributions to unsampled locations in the system. These developments are tested on a field application relying on a set of particle-size data observed within an alluvial aquifer in the Neckar river valley, in Germany.

## Keywords

Geostatistics Functional compositions Clustering Particle-size curves Groundwater Hydrogeology## Notes

### Acknowledgments

Financial support of MIUR (Project “Innovative methods for water resources under hydro-climatic uncertainty scenarios”, PRIN 2010/2011) is gratefully acknowledged. Support from the European Union’s Horizon 2020 Research and Innovation programme (Project “Furthering the knowledge Base for Reducing the Environmental Footprint of Shale Gas Development” FRACRISK—Grant Agreement No. 640979) is also acknowledged.

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